1. Nuclear Isovector Equation-of-State (EOS) and Astrophysics Hermann Wolter Dep. f. Physik, LMU Topics: 1.Phase diagram of strongly interacting matter and exploration via heavy ion collisions 2.Symmetric and asymmetric EoS, density dependence of symmetry energy 3.Description of Heavy Ion collisions with transport equations 4.Some results from HI studies 5.Comparison to neutron star observables 6.Summary and Outlook

2. Connection to Universe Cluster EoS, esp. Symmetry energy at high density Interpretation of heavy ion collision exp. (Astrophysical reaction rates by indirect methods)

4. Schematic Phase Diagram of Strongly Interacting Matter Quark-hadron coexistence Liquid-gas coexistence SIS

5. Schematic Phase Diagram of Strongly Interacting Matter Liquid-gas coexistence Quark-hadron coexistence Z/N 1 0 SIS neutron stars Exotic nuclei

6. Theoretical Treatment of Nuclear Matter V ij Non-relativistic: Hamiltonian H =  T i +  V ij, ; V nucleon-nucleon interaction Comparisons of calculations: Empirical saturation point Relativistic: Hadronic Lagrangian  nucleon, resonances  mesons

7. The nuclear EoS-Uncertainties stiff soft C. Fuchs, H.H. Wolter, WCI book, EPJA 30 (2006 )5 the nuclear EoS iso-stiff iso-soft Symmetry energy E symm [MeV]

8. Transport Descriptions of Heavy Ion Collisions Heavy ion collisions -> Non-Equilibrium Phenomena -> Transport Theory

9. Transport description of heavy ion collisions: For Wigner transform of the one-body density: f(r,p;t) Vlasov eq.; mean field2-body hard collisions loss termgain term 1 11 1 2 34 Simulation with Test Particles: Hamiltonian EoM test particles

10. High Density Symmetric Nuclear Matter Observables V2: Elliptic flowV1: Sideward flow T.Gaitanos, Chr. Fuchs, Nucl. Phys. 744 (2004)

11. Isospin Transport through Neck: Rami imbalance ratio: asysoft eos superasystiff eos experimental data ( B. Tsang et al. PRL 92 (2004) ) ASYSOFT EOS – FASTER EQUILIBRATION Baran, Colonna, Di Toro, Zielinska- Pfabe, Wolter, PRC 72 (2005) 064620

12. Kaon Production: A good way to determine the symmetric EOS (C. Fuchs, A.Faessler, et al., PRL 86(01)1974) Also useful for Isovector EoS? -charge dependent thresholds - in-medium effective masses -Mean field effects Main production mechanism: NN  BYK, pN  YK

13. Astrophysical Implications of Iso-Vector EOS Neutron Star Structure Constraints on the Equation-of-state - from neutron stars: maximum mass gravitational mass vs. baryonic mass direct URCA process mass-radius relation - from heavy ion collisions: flow constraint kaon producton Equations of State tested: Klähn, Blaschke, Typel, Faessler, Fuchs, Gaitanos,Gregorian, Trümper, Weber, Wolter, Phys. Rev. C74 (2006) 035802

14. Neutron star masses and cooling and iso-vector EOS Tolman-Oppenheimer-Volkov equation to determine mass of neutron star Proton fraction and direct URCA Onset of direct URCA Forbidden by Direct URCA constraint Typical neutron stars Heaviest observed neutron star

15. Further Neutron Star Constraints: Mass-Radius Relation: Gravitational vs. Baryon Mass

16. Maximum massDirect Urca Cooling limit Mass-Radius Relations Gravitational vs. Baryon Mass Heavy Ion Collision obsevables

17. Summary and Outlook: 1.Equation of State at high densities can be tested in the laboratory in heavy ion collisions 2.Symmetry Energy (neutron matter) is particularly uncertain 3.Is important for the structure of exotic nuclei (nucleosynthesis) and for astrophysics 4.Comparison to neutron star observables (not completely satisfactory, yet); also supernovae Collaborators: C. Fuchs (Tübingen), T. Gaitanos (Giessen) D. Blaschke, et al., (Rostock-Breslau) M. Di Toro, M. Colonna, et al., (LNS Catania)